Generalized linear complementarity problems |
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Authors: | M Seetharama Gowda Thomas I Seidman |
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Institution: | (1) University of Maryland Baltimore County, 21228 Catonsville, MD, USA |
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Abstract: | It has been shown by Lemke that if a matrix is copositive plus on
n
, then feasibility of the corresponding linear complementarity problem implies solvability. In this article we show, under suitable conditions, that feasibility of ageneralized linear complementarity problem (i.e., defined over a more general closed convex cone in a real Hilbert space) implies solvability whenever the operator is copositive plus on that cone. We show that among all closed convex cones in a finite dimensional real Hilbert Space, polyhedral cones are theonly ones with the property that every copositive plus, feasible GLCP is solvable. We also prove a perturbation result for generalized linear complementarity problems.This research has been partially supported by the Air Force Office of Scientific Research under grants #AFOSR-82-0271 and #AFOSR-87-0350. |
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Keywords: | Linear complementarity problems polyhedral cones copositive plus thin cone |
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